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{(x,y) / x y=2x where x and y are positive integers }is a) Reflexive b) Symmetric c) transitive d) equivalence?
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{(x,y) / x y=2x where x and y are positive integers }is a) Reflexive b...
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The given relation is {(x,y) / x y=2x where x and y are positive integers}. We need to determine whether the relation is reflexive, symmetric, transitive or an equivalence relation.
Reflexive
A relation R is reflexive if for every a in A, (a,a) ∈ R. In other words, every element of the set is related to itself.
In this case, (1,2) ∈ R because 1 x 2 = 2 x 1. Therefore, the relation is not reflexive because (1,1) ∉ R.
Symmetric
A relation R is symmetric if for every (a,b) ∈ R, (b,a) ∈ R. In other words, if a is related to b, then b is related to a.
In this case, if (a,b) ∈ R, then a x b = 2a, and if (b,a) ∈ R, then b x a = 2b. Therefore, for (a,b) ∈ R, we have b = 2 and a = 1, and for (b,a) ∈ R, we have a = 2 and b = 1. Since (1,2) ∈ R but (2,1) ∉ R, the relation is not symmetric.
Transitive
A relation R is transitive if for every (a,b) and (b,c) ∈ R, (a,c) ∈ R. In other words, if a is related to b and b is related to c, then a is related to c.
In this case, let (a,b) and (b,c) ∈ R, then a x b = 2a and b x c = 2b. Multiplying the two equations, we get a x b x c = 4a, which implies (a,c) ∈ R. Therefore, the relation is transitive.
Equivalence
A relation R is an equivalence relation if it is reflexive, symmetric, and transitive.
Since the given relation is not reflexive and not symmetric, it is not an equivalence relation.
Conclusion
The given relation {(x,y) / x y=2x where x and y are positive integers} is not reflexive, not symmetric, and transitive. Therefore, it is not an equivalence relation.
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{(x,y) / x y=2x where x and y are positive integers }is a) Reflexive b...
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{(x,y) / x y=2x where x and y are positive integers }is a) Reflexive b) Symmetric c) transitive d) equivalence?
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{(x,y) / x y=2x where x and y are positive integers }is a) Reflexive b) Symmetric c) transitive d) equivalence? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about {(x,y) / x y=2x where x and y are positive integers }is a) Reflexive b) Symmetric c) transitive d) equivalence? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for {(x,y) / x y=2x where x and y are positive integers }is a) Reflexive b) Symmetric c) transitive d) equivalence?.
{(x,y) / x y=2x where x and y are positive integers }is a) Reflexive b) Symmetric c) transitive d) equivalence? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about {(x,y) / x y=2x where x and y are positive integers }is a) Reflexive b) Symmetric c) transitive d) equivalence? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for {(x,y) / x y=2x where x and y are positive integers }is a) Reflexive b) Symmetric c) transitive d) equivalence?.
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